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Sub-critical and Super-critical Regimes in Epidemic Models of Earthquake Aftershocks

Abstract : We present an analytical solution and numerical tests of the epidemic-type aftershock (ETAS) model for aftershocks, which describes foreshocks, aftershocks and mainshocks on the same footing. The occurrence rate of aftershocks triggered by a single mainshock decreases with the time from the mainshock according to the modified Omori law K/(t+c)^p with p=1+theta. A mainshock at time t=0 triggers aftershocks according to the local Omori law, that in turn trigger their own aftershocks and so on. The effective branching parameter n, defined as the mean aftershock number triggered per event, controls the transition between a sub-critical regime n<1 to a super-critical regime n>1. In the sub-critical regime, we recover and document the crossover from an Omori exponent 1-theta for t0, we find a novel transition from an Omori decay law with exponent 1-theta fot tt*. The case theta<0 yields an infinite n-value. In this case, we find another characteristic time tau controlling the crossover from an Omori law with exponent 1-theta for t
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https://hal.archives-ouvertes.fr/hal-00023347
Contributor : Agnès Helmstetter <>
Submitted on : Wednesday, January 27, 2021 - 10:11:44 AM
Last modification on : Thursday, January 28, 2021 - 3:02:09 AM
Long-term archiving on: : Wednesday, April 28, 2021 - 6:29:06 PM

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A. Helmstetter, D. Sornette. Sub-critical and Super-critical Regimes in Epidemic Models of Earthquake Aftershocks. Journal of Geophysical Research : Solid Earth, American Geophysical Union, 2002, 107, pp.2237. ⟨10.1029/2001JB001580⟩. ⟨hal-00023347⟩

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